Dynamics of complex feedback architectures in metabolic pathways

International audienceCellular metabolism contains intricate arrays of feedback control loops. These are a key mechanism by which cells adapt their metabolism to survive environmental disturbances. Gene regulation, in particular, typically displays complex architectures that combine positive and negative feedback loops between metabolites and enzymatic genes. Yet because of strong nonlinearities and high-dimensionality, it is challenging to determine the closed-loop dynamics of a given feedback architecture. Here we present a novel technique for the analysis of metabolic pathways under gene regulation. Our theory blends ideas from timescale separation and piecewise affine dynamical systems, applied to a wide class of unbranched metabolic pathways under steep nonlinear feedback. We propose a systematic method to construct a state transition graph for a given regulatory architecture, from where candidate closed-loop dynamics can be singled out for further analysis. The method recasts a high-dimensional nonlinear system into a piecewise affine system defined on a polytopic partition of the state space. In its most general setup, our theory allows to characterize the dynamics of pathways of arbitrary length, with any number of regulators, and under any combination of positive and negative feedback loops. We illustrate our results on an exemplar system that displays a stable limit cycle and bistable dynamics. We also discuss the implications of our results for the design of gene circuits in synthetic biology and metabolic engineering